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A201415 Decimal expansion of greatest x satisfying 6*x^2 = sec(x) and 0 < x < Pi.

%I A201415 #10 Nov 26 2024 21:07:43
%S A201415 1,4,9,6,2,8,5,0,4,8,6,0,7,6,5,2,9,5,3,4,7,9,2,2,9,0,4,1,7,1,2,4,2,4,
%T A201415 4,6,9,7,5,1,2,6,6,2,6,7,9,8,7,7,1,8,2,6,4,4,9,4,1,4,8,6,8,8,7,0,5,6,
%U A201415 1,9,9,3,2,4,9,0,6,9,7,4,6,1,6,1,7,7,7,6,8,9,8,5,8,6,6,4,9,0,8
%N A201415 Decimal expansion of greatest x satisfying 6*x^2 = sec(x) and 0 < x < Pi.
%C A201415 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201415 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201415 least:  0.42800895010041097002739347769069180659...
%e A201415 greatest: 1.496285048607652953479229041712424469...
%t A201415 a = 6; c = 0;
%t A201415 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201415 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201415 r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
%t A201415 RealDigits[r]    (* A201414 *)
%t A201415 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201415 RealDigits[r]    (* A201415 *)
%o A201415 (PARI) solve(x=1,2, 6*x^2*cos(x)-1) \\ _Charles R Greathouse IV_, Nov 26 2024
%Y A201415 Cf. A201397.
%K A201415 nonn,cons
%O A201415 1,2
%A A201415 _Clark Kimberling_, Dec 01 2011